| Last revised 1999/08/24 |
Since the problems are graded for technique and not for correctness, you can work with each other on the assignments. You should do so. You may also consult others outside the class, but I strongly advise against looking at their solutions before attempting the problems yourself. You must write up your own final copy, unless I have stated otherwise (no Xeroxes!).
| # | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Due | Sept. 9 |
Sept. 16 |
Sept. 23 |
Sept. 30 |
Oct. 7 |
Oct. 14 |
Oct. 21 |
Oct. 28 |
Nov. 4 |
Nov. 11 |
Nov. 18 |
None | Dec. 2 |
Dec. 8 |
| Chapters | 1 | 2 | 2, 4 | 4, 5 | 5 | 6 | 7 | 8 | 9 | 10, 11 | 11, 12 | -- | 13 | 14, 16 |
| Hints for | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | -- | 13 | 14 |
| Answers for | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | -- | 13 | 14 |
| Solutions for | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | -- | 13 | 14 |
HRW pp. 8-10 # 1, 16, 39; sheet # I and II, below.
In # 39(b), you need get an approximate answer only.
|
I. [Modified from Tipler's text] The period
T of a simple pendulum depends on the length L of
the pendulum and the acceleration of gravity g (dimensons
length/time2).
(a) Find a simple combination of L and g that has the dimensions of time. (b) Check the dependence of the period T on the length L by measuring the period (the time for a complete to-and-fro swing) of a pendulum for two different values of L. [Tie anything handy (an eraser, a book, ...) to a string and measure times with a watch. Great accuracy is not needed. You may use group data if you participated in getting it (serving as pendulum included).] (c) The correct formula relating T to L and g involves a constant that is a multiple of pi and cannot be obtained by the dimensional analysis in the first part of the problem. Using the value g = 9.8 m/s2 and your experimental results from above, find the formula relating T to L and g. |
|
II. [From Tipler's text] A ball thrown horizontally
from a height H with speed v travels a total
horizontal distance R.
(a) Do you expect R to increase or decrease with increasing H? With increasing v? (b) From dimensional analysis, find a possible dependence of R on H, v, and g. |
| Assigned Problems | 16 | 39 |
|---|---|---|
| Useful practice problems | 3-8, 19-21 | 33, 34 |
HRW pp. 28-35 # 11, 12, 15, 17, 19, 21, 23, 48, 87; sheet # III, below.
| III. A car travelling at v1 on an Interstate highway pulls out to pass a second car, which is travelling at v2 a distance d ahead of the first. Choosing the moment that the car pulls out to be t=0 and its position at that time to be x=0, where and when will the two cars be exactly abreast? Assume that neither car changes speed. |
Problem 15 requires a clever solution, not a long one. [Translation: problem 15 is a trick question.]
In 48 and 87, either work the problem symbolically and then substitute the given numbers, or work the problem first using the numbers and again using symbols only.
These problems are not lengthy and most are not difficult, so practice writing out very clear and organized solutions.
| Assigned Problems | 48, 87 |
|---|---|
| Useful practice problems | 34-38 |
HRW pp. 28-35 # 24, 28, 57, 58, 72.
For the first three problems, either work the problem symbolically and then substitute the given numbers, or work the problem first using the numbers and again using symbols only.
| Assigned Problems | 28 | 57, 58 | 72 |
|---|---|---|---|
| Useful practice problems | 27 | 56 | 52 |
HRW pp. 72-80 question 9 and problems 38, 53, 54, 56, and problem IV, below.
|
IV. (Modified from HRW fourth edition) A man wants to
cross a river a distance w wide. His rowing speed (relative
to the water) is vb and the river flows at a speed
of vr . The man rows at a heading which is an angle
theta away from straight across the river.
(a) How far down the bank of the river does he reach the other side? (b) How long does it take him to get across? Hint: when considering his rowing speed and heading, think only about the water and ignore the bank of the river. Think of him as being completely out of sight of land in a dense fog. |
For problems 53 and 56, either work the problem symbolically and then substitute the given numbers, or work the problem first using the numbers and again using symbols only.
| Assigned Problems | 24, 38, 53, 54, 56 |
|---|---|
| Useful practice problems | 18, 20, 22, 26, 28 |
HRW pp. 72-80 # 69, 91; sheet # V, VI, and VII, below.
(Don't miss the problems from Chapter 5, listed below.)
|
V. (Modified from HRW fourth edition) A man wants
to cross a river a distance w wide. His rowing speed
(relative to the water) is vb . The river
flows at a speed of vr , and the man's walking
speed on shore is vw .
(a) Find the path (combined rowing and walking) he should take to get to the point opposite his starting point in the shortest possible time. (b) How long does it take? Hint: the man can change only the angle at which he rows the boat. |
|
VI. (Modified from Tipler's text) A particle moves
clockwise in a circle of radius r with its center at (x, y) =
(r, 0). The particle starts from rest at the origin at time
t = 0. Its speed increases at the constant rate of b
in m/s2. [If you wish to do a trial run of the solution
with numbers, use r = 1 m and b = pi/2
m/s2.]
(a) How long does it take the particle to travel halfway around the circle? (b) What is its speed at that time? (c) What is the direction of its velocity at that time? (d) What are its radial and tangential acceleration then? (e) What are the magnitude and direction of the total acceleration halfway around the circle? |
|
VII. (Modified from Tipler's text) The position of a particle is given by
r = (3 m) sin (2 pi t) i + (2m) cos (2 pi t) j
where t is in seconds.
(a) Plot the path of the particle in the xy plane. (b) Find the velocity vector. (c) Find the acceleration vector and show that its direction is along r , so that the acceleration is radial. (d) Find the times when the speed is a maximum or minimum. |
| Assigned Problems | 69 | IV |
|---|---|---|
| Useful practice problems | 58-60, 62, 64, 67 | 77-80, 82, 83, 86 |
| Exam 1 covers all material to this point. Go to list of old exams |
HRW pp. 99-107 # 10, 11.
On numerical problems, give algebraic as well as numerical answers.
HRW pp. 99-107 # 39, 40, 54, 60, 73; sheet # VIII., below.
| VIII. (From Tipler's text) In a tug-of-war, two boys pull on a rope, each trying to pull the other over a line midway between their original positions. According to Newton's third law, the forces exerted by each boy on the other are equal and opposite. Show with a force diagram how one boy can win. |
On numerical problems, give algebraic as well as numerical answers.
HRW pp. 122-129 # 27, 36, 43 [check the hints page], 70; sheet #IX, X, and XI, below.
IX. (From a previous edition of HRW) The blocks shown in the figure on the
left are connected by cords that pass over frictionless pulleys. The
acceleration a of the system is known and is nonzero. What
is the magnitude of the frictional force on the block that slides
horizontally?
|
| X. (By Jack Uretsky) A 75-kg skier stands on a horizontal, snowy surface. The coefficient of friction is 0.02. The skier's friend pushes her with a steady force of 1 N. Calculate the acceleration of the skier. Check to make sure that your answer makes sense. |
|
XI. (Daniel Kleppner and Robert J. Kolenkow, An Introduction to Mechanics,
problem 2.37)
The "Eureka Hovercraft Corporation" wanted to hold hovercraft races as an advertising stunt. The hovercraft supports itself by blowing air downward, and has a big fixed propeller on the top deck for forward propulsion. Unfortunately, it has no steering equipment, so that the pilots found that making high speed turns was very difficult. The company decided to overcome this problem by designing a bowl-shaped track in which the hovercraft, once up to speed, would coast along in a circular path with no need to steer. They hired an engineer to design and build the track, and when he finished, he hastily left the country. When the company held their first race, they found to their dismay that the craft took exactly the same time T to circle the track, no matter what its speed. Find the equation for the cross section of the bowl in terms of T. [Hint: At least find the slope of the track as a function of the horizontal distance from the center of the circle.] |
On numerical problems, give algebraic as well as numerical answers.
HRW pp. 149-154 # 24, 27, 29, 31 [the force involved is conservative], 40, 50; Sheet # XII, below.
| XII. (From a previous edition of HRW) A force F in the direction of increasing x acts on an object moving along the x axis. If the magnitude of the force is F = 10 e -x / 2.0 N, where x is in meters, find the work done by F as the object moves from x = 0 to x = 2.0 m (a) by plotting F(x) and finding the area under the curve and (b) by integrating to find the work analytically. |
On numerical problems, give algebraic as well as numerical answers.
HRW pp. 176-185 # 10 and 39 together, 40, 44, 46, 49, 75.
| Exam 2 covers all material to this point. Go to list of old exams |
On numerical problems, give algebraic as well as numerical answers.
HRW pp. 207-213 # 11, 16, 40, 47, 55.
In number 47, define the relative velocity as the difference in the
velocities of the boat and of the thrown object(s) after the
throw is completed.
HRW pp. 231-237 # 27, 55, 67, 68.
HRW pp. 260-267 # 7, 19, 44, 59.
HRW pp. 288-296 # 15, 33, 41, 69.
|
Exam 3 covers all material to this point. Go to list of old exams |
HRW pp. 315-321 # 15, 20, 24, 26, 29, 41, 45.